Equations Reducible to a Pair of Linear Equations in Two Variables

Q.

The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs. 105 and for a journey of 15 km, the charge paid is Rs. 155. What are the fixed charges and the charge per kilometer? How much does a person have to pay for travelling a distance of 25 km?

Q. A two-digit number is 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.

1. 24
2. 25
3. 26
4. 27

Q.

Abdul travelled 300 km by train and 200 km by taxi taking 5 hours 30 minutes.But, if he travels 260 km by train and 240 km by taxi, he takes 6 minutes longer.Find the speed of the train and that of the taxi.

Q. A fraction becomes 1/3 if 1 is subtracted from both its numerator and denominator. It 1 is added to both the numerator and denominator, it becomes 1/2. Find the fraction.

Q. Points A and B are 90 km apart from each other on a highway. A car starts from A and another from B at the same time. If they go in the same direction they meet in 9 hours and if they go in opposite direction they meet in $\frac{9}{7}$ hours. Speed of car starting from point A is:

1. 30 km/hr
2. 90 km/hr
3. 40 km/hr
4. 220 km/hr

Q. A man walks a certain distance with certain speed. If he walks 1/2 km an hour faster, he takes 1 hour less. But, if he walks 1 km an hour slower, he takes 3 more hours. Find the distance covered by the man and his original rate of walking.

Q.

If $2^{x+y}=2^{x-y}=\sqrt{8}$ then the value of y is

(a) $\frac{1}{2}$ (b) $\frac{3}{2}$ (c) 0 (d) none of these

Q.

The car hire charges in a city comprise of a fixed charges together with the charge for the distance covered. For a journey of 12 km, the charge paid is Rs 89 and for a journey of 20 km, the charge paid is Rs 145. What will a person have to pay for travelling a distance of 30 km?

Q.

A man travels 600 km to his home , partly by train and partly by bus.If he travels 120km by train and rest by bus it would take 8hours.If he travels 200km by train and rest by bus it will take 20 minutes more .find speed of train and bus saparetly.

Q. The sum of a two digit number and the number obtained by reversing the order of its digits is 99. If the digits differ by 3, find the number.

Q.

A taxi charges in a city comprise of a fixed charge together with charge for distance covered. For a journey of 10km the charge paid was 75Rs and for 15km the charge was 110Rs. Find the charge for 25km.

Q.

A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was Rs. 1500 after 4 years of service andRs. 1800 after 10 years of service, what was his starting salary and what is the annual increment?

Q.

Ten years ago, the sum of the ages of two sons was one third of their father's age.One son is two years older than the other and sum of their present ages is 14 years less than the father's present age. Find the present ages of all.

Q.

By increasing the speed of a car by 10km/hr, the time of journey for a distance of 72km is reduced by 36mins. Find the original speed.

1. 15 km/hr

2. 36 km/hr

3. 30 km/hr

4. 72 km/hr

5. 60 km/hr

Q.

In an examination, one mark is awarded for every correct answer, while 1/4 mark is deducted for every wrong answer. A student answered 120 questions and got 20 marks. Which of the following pair of equations would give the result for how many questions did he answered correctly?

1. x + y = 120; - x + 4y = 80

2. x + y = 60; x + 4y = 80

3. x + y = 120; 4x + 3y = 80

4. x + y = 120; 3x + 4y = 80

Q. A passenger while boarding the plane slippe from the stairs and got hurt. the pilot took the passengers in the emergency clinic at the airport for the treatment due to this, plane got delayed half an hour. To reach the destination 1500km away in time, so that the passengers could catch the connection flight, the speed of the plane was increased by 250km/hr than the usual speed. What is the usual speed of the plane.

Q. The ratio between the length and the breadth of a rectangle field is 3 : 2. If only the length is increased by 5 metres , the new area of field will be 2600 sq. metres . What is the breadth of the rectangle field?

Q.

Solve the following pair of equation

$\frac{5}{x-1}$ + $\frac{1}{y-2}$ = 2

$\frac{6}{x-1}$ - $\frac{3}{y-2}$ = 1

1. 4, 5

2. 1/3, 1/3

3. None of these

4. 5, 3

Q. 4 CD's and 3 pen drives cost ₹1100 while 3 CD's and 7 pen drives cost ₹2250. The cost of 2 CD's and 3 pen drives is

1. ₹1400
2. ₹1100
3. ₹1000
4. ₹890

Q.

Ramesh travels 760km to his home partly by train and partly by car . He takes 8 hours if he travels 160km by train and the rest by car .he takes 12 minutes more if he travels 240km by train and the rest by car . Find the speed of the train and car respectively.

Q.

customers are asked to stand in the lines. if one customer is extra in a line , then there would be two less lines . if one customer is less in line , there would be three more lines . find number of customers

Q. In a painting competition of a school a child made lndian flag whose perimeter was 50cm.lts area will be decreased by 6square cm, if length is decreased by 3cm and breadth is increased by 2cm, then find the dimensions of the flag?

Q.

There are two examination rooms A and B. If 10 candidates are sent from A to B, the number of students in each room is same. If 20 candidates are sent from B to A, the number of students in A is double the number of students in B. Find the number of students in each room.

Q. Write the condition to be satisfied by q so that a rational number $\frac{p}{q}$has a terminating decimal expansion.

Q.

Out of $1900km$, Vishal travelled some distance by bus and some by aeroplane. Bus travels with average speed $60km/hr$ and the average speed of aeroplane is $700km/hr$. It takes $5$ hours to complete the journey. Find the distance, Vishal travelled by bus.

Q.

Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?

Q.

The numbers_ and_ are their own reciprocals.

Q.

The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number.

Q.

In x class, if three students sit on bench, one student will be left. If four students sit on each bench, one bench will left. Find the number of students and number of benches in class.

Q. A SHOPKEEPER BUYS A NUMBER OF BOOKS FOR RS.1200.IF HE HAD BOUGHT 10 MORE BOOKS FOR THE SAME AMOUNT, EACH BOOK WOULD HAVE COST HIM RS.20 LESS..HOW MANY BOOKS DID HE BUY?